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Question

In the morning , Amy had 4/5 as much money as Ben  and $36 more than Carl. In the afternoon,
after Amy and Ben each gave 1/3 of their money to Carl, Carl had four times as much money as what he had in the morning.

a) Who had the most and who had the least amount of money in the afternoon

b) find the difference in the amount of money that the two persons in Part(a) had in the afternoon

Answer

(a)
In the morning —
Amy : 4 x 3 = 12 units
Ben : 5 x 3 = 15 units
Carl : 12 units – 36

In the afternoon —
Amy : 12 – (1/3) x 12 = 8 units
Ben : 15 – (1/3) x 15 = 10 units
Carl : (12 + 4 + 5) units – 36 = 21 units – 36

21 units – 36 = (12 units – 36) x 4 = 48 units – 144
1 unit = (144 – 36)/(48 – 21) = 4
8 x 4 = 32 (Amy has the least)
10 x 4 = 40 (Ben)
21 x 4 – 36 = 48 (Carl has the most)

(b)
48 – 32 = 16

Ans : (a) Carl has the most and Amy has the least; (b) $16.

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This is a Before After question. 

LCM

4/5 = 12/15

   Before Transfer After
Amy 12u – 4u 8u
Ben 15u – 5u 10u
Carl 12u – 36 + 9u 21u – 36

(12u – 36)/1  = (21u – 36)/ 4

48u – 144 = 21u – 36

48u – 21u = 144 – 36

27u = 108

1u = 108 ÷ 27 = 4

 a)

Ben has the  most.

Any has the least.

b)

15u – 8u = 7u

7u = 7 × 4 = 28

 

 

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